Magic angles of twisted three-leaf graphene

We consider a configuration of three stacked graphene monolayers with identical consecutive twist angles θ. It is noteworthy that in the chiral limit, when interlayer coupling conditions between the AA regions of the moire pattern are neglected, we find four perfectly flat bands (for each valley) with a sequence of magic angles that are exactly equal to the magic angles of twisted bilayer graphene (TBG). divide by 2–√. Therefore, the first magic angle for equal twist trilayer graphene (eTTG) in the chiral limit is θ∗≈1.05∘/2–√≈0.74∘. We prove this relation analytically and show that the Bloch states of the eTTG flat bands are nonlinearly related to the TBG states. In addition, we show that at magic angles, the top and bottom zones must touch four exactly flat zones at the Dirac point of the middle graphene layer. Finally, we examine the eTTG spectrum beyond the chiral limit through numerical analysis.